Summer \(T_s\) \[ \frac{dn}{d\tau} = n(1-n) - \frac{n^2p}{\tilde{b}^2+n^2}, \\ \frac{dp}{d\tau} = \tilde{\gamma} \frac{n^2p}{\tilde{b}^2+\tilde{n}^2} + \tilde{s}\frac{p}{1+\tilde{\nu}p}-\tilde{m}p \]
Winter \((1-T_s)\) \[ \frac{dn}{d\tau} = - \frac{\tilde{\alpha}np}{\tilde{\beta}+n}, \\ \frac{dp}{d\tau} = \tilde{\gamma} \frac{\tilde{\alpha}np}{\tilde{\beta}+n}-\tilde{\mu}p \]
| Parameter | Description |
|---|---|
| \(r\) | Prey summer growth rate |
| \(K\) | Prey carrying capacity |
| \(\alpha\) | Specialist saturation killing rate |
| \(\beta\) | Specialist halg-saturation |
| \(\gamma\) | Predator-prey ration constant |
| \(\mu\) | Winter predator death rate |
| \(s-m\) | Predator intrinsic population growth |
| \(\nu\) | Generalist density dependence |
How does stochasticity in season length (\(T_s\)) affecr the system’s dynamics? Can it alter periodicity or amplitude?
What type of dynamics can be expected under the current rate of climate change?
The wavelet power spectra of the simulated time series of predator-prey dynamics with added variabilty to \(T_s\)
Relatively small perturbations in the length of the season lead to irregular oscillation regimes (Fig. 2-4)